On Integrable Backgrounds Self-dual under Fermionic T-duality

Amit Dekel; Ido Adam; Yaron Oz

REVIEW

On Integrable Backgrounds Self-dual under Fermionic T-duality

Ido Adam, Amit Dekel, Yaron Oz

High Energy Physics - Theory · Submitted 22 Feb 2009 · 22 references

Pith's verdict: The explicit PSU self-duality computations are solid and worth having; the 'general' criterion in section 4 is a heuristic that doesn't deliver what the abstract advertises.

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arXiv ID0902.3805 (version 4)

Pith IDYMYHRT6S, Pith's permanent record of this paper and its review

CitationAmit Dekel, Ido Adam, Yaron Oz. "On Integrable Backgrounds Self-dual under Fermionic T-duality." arXiv:0902.3805 (2009). https://pith.science/paper/YMYHRT6S

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Quick read on 0902.3805. The useful part is the concrete algebra, not the general story the abstract sells. Sections 2.1 and 2.2 do the Buscher procedure honestly for AdS2×S2 and AdS3×S3: gauge fields in, integrated out, dual action mapped back to the original by a written-out automorphism plus change of variables (2.12)-(2.13), (2.32)-(2.33), with a clean Jacobian argument via vanishing supertrace (2.14). I checked the structure and it holds together. The negative results in section 3 are also done case by case with explicit singular matrices, which is convincing for the named models even if the surrounding prose is loose. That's a real contribution: knowing that the OSp family, including the ABJM-dual AdS4×CP3, fails the fermionic T-duality test is worth having in the literature, and it's the kind of thing people will cite when they want to know which integrable backgrounds have a dual superconformal symmetry and which don't. The appendices reproduce the superalgebras carefully, which makes the computations checkable. Credit where due: this is honest, explicit work. Now the soft spot, and it's the one the stress test flags. Section 4's step from M = m + O(χ²) to M^{-1} = m^{-1} + O(χ²) presupposes m is invertible; for a generic singular m, an O(χ²) correction makes M invertible. The paper needs to show the corrections preserve the kernel of m — the R-symmetry representation argument for AdS4×CP3 gestures at this but doesn't demonstrate it. 'All the fermions should cancel' is not a proof. So the abstract's 'general algebraic argument' [abstract:s2] overstates what section 4 delivers; it's a heuristic that organizes the case-by-case results, not an independent criterion. The paper is also honest about its own limitations: footnote 1 concedes the AdS2×S2 model isn't a genuine critical superstring, section 3.3 concedes the partial gauge-fixing, and section 3.1 offers the κ-symmetry-exactness explanation as a 'possible' one. Those are stated, not hidden, and I'd weigh them as acknowledged rather than as new findings. Bottom line: the specific positive and negative results stand on their own algebra and don't depend on section 4. The general criterion needs either a real proof or a demotion to 'pattern'. Worth a serious referee — the computations deserve checking by someone who will go through the commutators — but I'd frame the ask as tightening section 4, not redoing sections 2 and 3.

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Major objections (3)

[§4, immediately after Eq. (4.11)] The step from M = m + O(χ²) to M⁻¹ = m⁻¹ + O(χ²) presupposes that m is invertible, which is exactly what the argument is trying to deny. For a generic singular matrix m, an O(χ²) correction makes M invertible, so singularity of m does not by itself imply singularity of M. The sentence 'all the fermions should cancel' asserts the conclusion rather than deriving it. To make the general criterion valid, the manuscript needs to show either that det M vanishes identically (e.g. by exhibiting a kernel vector of M that is preserved by the fermionic corrections) or that the corrections are constrained by the R-symmetry representation structure — as is hinted for the odd-dimensional representation in the AdS4×CP3 case — to preserve ker(m). As written, the general criterion is heuristic, and the abstract's claim [abstract:s2] of 'a general algebraic argument' overstates what §4 delivers. Either supply the missing step or downgrade §4 to a heuristic and let the explicit computations of §3 carry the negative results.
[§3.1, discussion following Eqs. (3.12)-(3.13)] The conclusion drawn for OSp(2|2) is that the Buscher procedure fails, not that no fermionic T-duality exists. The manuscript itself offers a gauge-dependent explanation for the failure — 'A possible explanation is that the quadratic term is κ-symmetry-exact' — and then exhibits a second κ-gauge (Eq. (3.14)) in which the quadratic term is absent altogether. This is an honest observation, but it means the negative claim for this background is a statement about a particular parameterization, not a no-go theorem. The abstract's flat assertion that these backgrounds 'are not' self-dual should be qualified accordingly, or gauge-independence of the obstruction should be established.
[§3.3, parenthetical after Eq. (3.24)] For the critical AdS4×CP3 background the negative conclusion rests on a partially κ-gauge-fixed coset model, and the manuscript acknowledges that 'this partial gauge-fixing is not compatible with all the string solutions so a general analysis would seem to require the use of the complete un-fixed sigma-model derived in [20]'. The subsequent justification — that broken supersymmetries are not isometries and so cannot participate in the T-duality — is plausible but not demonstrated. Because this is the flagship critical background of the paper, the caveat should either be resolved (e.g. by repeating the analysis in the complete superspace of [20]) or be stated explicitly in the abstract and conclusions, so that the reader does not take the no-go as established for the full string.

Minor objections (6)

[Eqs. (2.13) and (2.33)] The change of variables as printed contains what appear to be typographical errors: in (2.13) 'y^i → y^i y^2' presumably means y^i → y^i/y^2, and in (2.33) 'y^2 → −y^2/y^2' literally evaluates to −1. Please correct these so the maps are well defined.
[Eq. (2.12)] The stated automorphism P↔K, D→−D, Q↔S, Q̂↔Ŝ, with all other generators fixed, should be checked explicitly against the bracket {Q_α,S_β} in (D.1): applying the map and using the cited identity appears to flip the sign of the R_{ij} term unless R_{ij} also transforms. Please state how R_{ij} transforms, or correct (2.12).
[Footnote 1] The footnote correctly notes that the AdS2×S2 superspace must be supplemented by an internal CFT and that it is not clear such a description exists. Since the self-duality result of §2.1 is a statement about this partial sigma model rather than about a consistent string background, it would help to say so in the main text as well.
[§3.4] The argument here is a zeroth-order expansion of the current in the fermions of B (Eq. (3.51)), and the conclusion is drawn from the structure at that order. Please state explicitly that this is a perturbative argument and indicate why higher orders cannot alter the conclusion.
[Eqs. (3.4)-(3.5)] The text says the action is 'quadratic in θ', but (3.4) also contains terms linear in θ, e.g. (1/y)ξ̄(∂θ∂̄x − ∂x∂̄θ). The quadratic statement refers only to the ∂θ∂̄θ term; please make this precise.
[References and front matter] Reference [12] is printed as 'j. Stefanski, B.'; the address reads 'Am M¨ulehnberg 1' rather than 'Mühlenberg'. These are typographical and should be corrected at proof stage.

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The paper

The paper claims

Fermionic T-duality self-duality holds for PSU supercoset sigma-models (AdS2 x S2, AdS3 x S3) but fails for OSp supercosets (non-critical AdS2, AdS4, AdS4 x CP3), with a general algebraic criterion proposed for the split.

The reading

String theory lives on curved backgrounds, and a long-standing question is which of these backgrounds have a hidden symmetry called fermionic T-duality. Ordinary T-duality swaps a small circle for a large one; the fermionic version does the same for the Grassmann-odd coordinates of a superspace. In 2008 Berkovits and Maldacena showed that the AdS5 x S5 background, the gravity dual of N=4 super Yang-Mills, is self-dual under a combination of bosonic and fermionic T-duality. That self-duality underlies the dual superconformal symmetry of planar scattering amplitudes. This paper asks how general the phenomenon is. The authors take integrable Green-Schwarz sigma-models on several anti-de Sitter backgrounds with Ramond-Ramond flux, all built as supercosets of Lie supergroups. For the PSU-based models, AdS2 x S2 and AdS3 x S3, they carry out the Buscher procedure explicitly: introduce gauge fields for an Abelian subalgebra of translations and supercharges, integrate them out, and show that the resulting dual action is mapped back to the original by an automorphism of the algebra plus a change of variables. The Jacobian is trivial because the similarity transformation has vanishing supertrace. For the OSp-based models, non-critical AdS2 with four supersymmetries, AdS4 with eight, and the critical AdS4 x CP3, the same procedure breaks down. The fermionic gauge fields appear only linearly in the action, or the matrix that multiplies them is singular, so the equations of motion cannot be solved. The authors trace this to the Cartan-Killing form of the ortho-symplectic group, which pairs only different Grassmann-odd generators. They close with a general algebraic argument for when the procedure should work and when it should fail.

Extended reading notes

Core claim

The paper claims that sigma-models based on supercosets of PSU supergroups, specifically AdS2 x S2 and AdS3 x S3, are self-dual under a combination of bosonic and fermionic T-duality, while supercosets of OSp supergroups, specifically non-critical AdS2 with four supersymmetries, AdS4 with eight supersymmetries, and the critical AdS4 x CP3 background, are not. It further claims a general algebraic argument for when a supercoset is expected to have a fermionic T-duality symmetry and when it will fail to have one (abstract:s1, abstract:s2).

Load-bearing premise

The general algebraic argument in section 4 rests on the step that the full matrix M multiplying the fermionic gauge fields has inverse M^{-1} = m^{-1} + O(chi^2), where m is the zeroth-order matrix, because 'all the fermions should cancel' (section 4, immediately after Eq. 4.11). This is asserted rather than proven. If higher-order fermion corrections could combine to make M invertible even when m is singular, the general failure criterion would not follow, and the negative results would have to be re-established case by case.

Original abstract

We study the fermionic T-duality symmetry of integrable Green-Schwarz sigma-models on AdS backgrounds with Ramond-Ramond fluxes in various dimensions. We show that sigma-models based on supercosets of PSU supergroups, such as AdS_2 \times S^2 and AdS_3 \times S^3 are self-dual under fermionic T-duality, while supercosets of OSp supergroups such as non-critical AdS_2 and AdS_4 models, and the critical AdS_4 \times CP^3 background are not. We present a general algebraic argument to when a supercoset is expected to have a fermionic T-duality symmetry, and when it will fail to have one.

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The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; show every role.

We study the fermionic T-duality symmetry of integrable Green-Schwarz sigma-models on AdS backgrounds with Ramond-Ramond fluxes in various dimensions. We show that sigma-models based on supercosets of PSU supergroups, such as AdS_2 \times S^2 and AdS_3 \times S^3 are self-dual under fermionic T-duality, while supercosets of OSp supergroups such as non-critical AdS_2 and AdS_4 models, and the critical AdS_4 \times CP^3 background are not. We present a general algebraic argument to when a supercoset is expected to have a fermionic T-duality symmetry, and when it will fail to have one.

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s0	We study the fermionic T-duality symmetry of integrable Green-Schwarz sigma-models on AdS backgrounds with Ramond-Ramond fluxes in various dimensions.	contribution 0.85	0.86	0.05	asserted 0.63
s1	We show that sigma-models based on supercosets of PSU supergroups, such as AdS_2 \times S^2 and AdS_3 \times S^3 are self-dual under fermionic T-duality, while supercosets of OSp supergroups such as non-critical AdS_2 and AdS_4 models, and the critical AdS_4 \times CP^3 background are not.	result 1.00	0.93	0.80	asserted 1.00
s2	We present a general algebraic argument to when a supercoset is expected to have a fermionic T-duality symmetry, and when it will fail to have one.	contribution 0.80	0.92	0.16	asserted 0.81

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.77.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (22)

[20]

J. Gomis, D. Sorokin, and L. Wulﬀ, The complete AdS(4) x CP(3) superspace for the type IIA superstring and D-branes , 0811.1566

View on Pith Pith review arXiv
[1]

L. F. Alday and J. M. Maldacena, Gluon scattering amplitudes at strong coupling , JHEP 06 (2007) 064, [ 0705.0303]

View on Pith Pith review arXiv 2007
[2]

J. M. Drummond, J. Henn, V. A. Smirnov, and E. Sokatchev, Magic identities for conformal four-point integrals , JHEP 01 (2007) 064, [ hep-th/0607160]

View on Pith Pith review arXiv 2007
[3]

J. M. Drummond, G. P. Korchemsky, and E. Sokatchev, Conformal properties of four-gluon planar amplitudes and Wilson loops , Nucl. Phys. B795 (2008) 385–408, [0707.0243]

View on Pith Pith review arXiv 2008
[4]

N. Berkovits and J. Maldacena, Fermionic T-Duality, Dual Superconformal Symmetry, and the Amplitude/Wilson Loop Connection , JHEP 09 (2008) 062, [0807.3196]

View on Pith Pith review arXiv 2008
[5]

N. Beisert, R. Ricci, A. A. Tseytlin, and M. Wolf, Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability , 0807.3228

View on Pith Pith review arXiv
[6]

I. Bena, J. Polchinski, and R. Roiban, Hidden symmetries of the AdS(5) x S**5 superstring, Phys. Rev. D69 (2004) 046002, [ hep-th/0305116]

View on Pith Pith review arXiv 2004
[7]

I. Adam, A. Dekel, L. Mazzucato, and Y. Oz, Integrability of type II superstrings on Ramond-Ramond backgrounds in various dimensions , JHEP 06 (2007) 085, [hep-th/0702083]

View on Pith Pith review arXiv 2007
[8]

J.-G. Zhou, Super 0-brane and GS superstring actions on AdS(2) x S(2) , Nucl. Phys. B559 (1999) 92–102, [ hep-th/9906013]

View on Pith Pith review arXiv 1999
[9]

J. Park and S.-J. Rey, Green-Schwarz superstring on AdS(3) x S(3) , JHEP 01 (1999) 001, [ hep-th/9812062]

View on Pith Pith review arXiv 1999
[10]

J. Rahmfeld and A. Rajaraman, The GS string action on AdS(3) x S(3) with Ramond-Ramond charge, Phys. Rev. D60 (1999) 064014, [ hep-th/9809164]. – 25 –

View on Pith Pith review arXiv 1999
[11]

G. Arutyunov and S. Frolov, Superstrings on AdS4xCP 3 as a Coset Sigma-model , JHEP 09 (2008) 129, [ 0806.4940]

View on Pith Pith review arXiv 2008
[12]

j. Stefanski, B., Green-Schwarz action for Type IIA strings on AdS4 × CP 3, Nucl. Phys. B808 (2009) 80–87, [ 0806.4948]

View on Pith Pith review arXiv 2009
[13]

P. Fre and P. A. Grassi, Pure Spinor Formalism for Osp(N—4) backgrounds , 0807.0044

View on Pith Pith review arXiv
[14]

G. Bonelli, P. A. Grassi, and H. Safaai, Exploring Pure Spinor String Theory on AdS4 × CP3, JHEP 10 (2008) 085, [ 0808.1051]

View on Pith Pith review arXiv 2008
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R. D’Auria, P. Fre, P. A. Grassi, and M. Trigiante, Superstrings on AdS4xCP 3 from Supergravity, 0808.1282

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T. H. Buscher, A Symmetry of the String Background Field Equations , Phys. Lett. B194 (1987) 59

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N. Berkovits, M. Bershadsky, T. Hauer, S. Zhukov, and B. Zwiebach, Superstring theory on AdS(2) x S(2) as a coset supermanifold , Nucl. Phys. B567 (2000) 61–86, [hep-th/9907200]

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O. Aharony, O. Bergman, D. L. Jaﬀeris, and J. Maldacena, N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091, [ 0806.1218]

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L. Frappat, P. Sorba, and A. Sciarrino, Dictionary on Lie superalgebras , hep-th/9607161

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Forward citations

Cited by 11 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Dualities for Loop Amplitudes of N=6 Chern-Simons Matter Theory
hep-th 2011-07 conditional novelty 7.0 of 10

The two-loop four-point amplitude of ABJM theory matches the two-loop Wilson loop in its divergent and log-squared terms, and mirrors the one-loop N=4 super Yang-Mills amplitude in functional form.
Tree-level Recursion Relation and Dual Superconformal Symmetry of the ABJM Theory
hep-th 2010-12 conditional novelty 7.0 of 10

A nonlinear momentum-shift recursion relation for 3D ABJM theory yields the first proof that all tree-level amplitudes are dual superconformal.
Conformal Twists, Yang-Baxter $\sigma$-models & Holographic Noncommutativity
hep-th 2017-05 conditional novelty 6.0 of 10

For every homogeneous Yang-Baxter deformation of AdS5, the open-string metric is undeformed AdS5 with constant coupling, and the noncommutativity tensor equals minus twice the deformation parameter times the r-matrix.
Scattering Amplitudes/Wilson Loop Duality In ABJM Theory
hep-th 2011-07 conditional novelty 6.0 of 10

The two-loop four-point amplitude in ABJM theory equals the two-loop light-like four-polygon Wilson loop up to a scheme-dependent constant, extending the amplitude/Wilson-loop duality to three dimensions.
Superstrings in AdS(2)xS(2)xT(6)
hep-th 2011-04 conditional novelty 6.0 of 10

The complete AdS2 x S2 x T6 superstring admits a Lax connection to quadratic order in fermions, truncates consistently to the PSU(1,1|2) supercoset, and yields a conjectured asymptotic Bethe ansatz for its massive states.

Show 6 more citing papers

Evidence for the classical integrability of the complete AdS(4) x CP(3) superstring
hep-th 2010-09 conditional novelty 6.0 of 10

A zero-curvature Lax connection is built for the AdS4 x CP3 superstring sector containing the eight broken-supersymmetry fermions, extending integrability evidence beyond the OSp(6|4) coset model.
Dual Superconformal Symmetry of N=6 Chern-Simons Theory
hep-th 2010-07 accept novelty 6.0 of 10

The four- and six-point tree amplitudes of N=6 Chern-Simons (ABJM) theory are invariant under an OSp(6|4) dual superconformal symmetry once three Grassmann-even dual coordinates are introduced, and the nontrivial dual...
Yangian Invariant Scattering Amplitudes in Supersymmetric Chern-Simons Theory
hep-th 2010-07 conditional novelty 6.0 of 10

An integral over a Grassmannian-like matrix is proposed to generate all 2k-point amplitudes of N=6 super-Chern-Simons theory, and is argued to be annihilated by the level-one Yangian generators for every k.
Light-like polygonal Wilson loops in 3d Chern-Simons and ABJM theory
hep-th 2010-04 conditional novelty 6.0 of 10

Two-loop light-like polygonal Wilson loops in 3d Chern-Simons theory develop UV divergences, and the ABJM four-cusp result reproduces the N=4 SYM functional form up to a constant.
Symmetries of Tree-level Scattering Amplitudes in N=6 Superconformal Chern-Simons Theory
hep-th 2010-03 conditional novelty 6.0 of 10

The four- and six-point tree-level scattering amplitudes of N=6 superconformal Chern-Simons theory are shown to be invariant under an osp(6|4) Yangian symmetry, extending integrability from the spectral problem to the...
Simplifying superstring and D-brane actions in AdS(4) x CP(3) superbackground
hep-th 2009-03 accept novelty 5.0 of 10

A particular kappa-symmetry gauge choice collapses the full 32-fermion AdS4 x CP3 supergeometry into explicit, relatively compact superstring and D-brane actions, including a T-dualized string action with fermions onl...

How the literature uses it

44 arXiv papers cite this in 71 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 47 sentences without a confident label

Contests it 1 paper

[ref] , fail to take account of the chirality and the results of ref.

A Requiem for $AdS_4 \times \mathbb{C} P^3$ Fermionic self-T-duality · Introduction · contest 0.88

Compares with it 3 papers

This means that self-duality in $D=10$ and self-duality in the supercoset formulation in $D=6$ presented in [ref] have a slightly different flavour.

Self-duality of the D1-D5 near-horizon · Geometry with RR-flux · 0.98
The earlier treatment of $AdS_2×S^2$ in [ref] studied only the coset $σ$-model $PSU(1,1|2)/U(1)^2$, rather than the whole critical string theory.

Fermionic T-Duality of $AdS_n \times S^n (\times S^n) \times T^m$ using IIA Supergravity · Case $α=1$: $AdS_2×S^2×T^6$ · 0.93
This should be contrasted with the usual prescription where bosonic T-dualities along translation isometries and fermionic T-dualities with respect to Poincaré Killing spinors feature [ref] (see also [ref] ).

Conformal Twists, Yang-Baxter $\sigma$-models & Holographic Noncommutativity · Introduction · 0.89

Cites it as support 1 paper

In fact, it has been argued in [ref] that the $OSp(6|4)$ supercoset subsector of the Green–Schwarz superstring in $AdS_4×CP^3$ does not have any fermionic T–duality symmetry since in $OSp(6|4)$ the dimension of the representation of the supercharges under the R–symmetry is odd.

Simplifying superstring and D-brane actions in AdS(4) x CP(3) superbackground · The fundamental string · 0.98

Cites it as background 16 papers

Related work on fermionic T-duality has appeared in [ref] .

Exploring Fermionic T-duality · Introduction · 0.98
Working with Green-Schwarz sigma-models, we have witnessed a few papers studying both critical and non-critical strings [ref] .

Fermionic T-duality: A snapshot review · Self-dual geometries · 0.98
At strong coupling this symmetry should rely on self–duality properties of type IIA string on $AdS_4 ×CP_3$ under a suitable combination of bosonic and fermionic T–dualities [ref] , even if the situation is complicated by the emergence of singularities in the fermionic T–transformations [ref] – [ref] .

Scattering in ABJ theories · Introduction · 0.81

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [20]

J. Gomis, D. Sorokin, and L. Wulﬀ, The complete AdS(4) x CP(3) superspace for the type IIA superstring and D-branes , 0811.1566

View on Pith Pith review arXiv

[2] [1]

L. F. Alday and J. M. Maldacena, Gluon scattering amplitudes at strong coupling , JHEP 06 (2007) 064, [ 0705.0303]

View on Pith Pith review arXiv 2007

[3] [2]

J. M. Drummond, J. Henn, V. A. Smirnov, and E. Sokatchev, Magic identities for conformal four-point integrals , JHEP 01 (2007) 064, [ hep-th/0607160]

View on Pith Pith review arXiv 2007

[4] [3]

J. M. Drummond, G. P. Korchemsky, and E. Sokatchev, Conformal properties of four-gluon planar amplitudes and Wilson loops , Nucl. Phys. B795 (2008) 385–408, [0707.0243]

View on Pith Pith review arXiv 2008

[5] [4]

N. Berkovits and J. Maldacena, Fermionic T-Duality, Dual Superconformal Symmetry, and the Amplitude/Wilson Loop Connection , JHEP 09 (2008) 062, [0807.3196]

View on Pith Pith review arXiv 2008

[6] [5]

N. Beisert, R. Ricci, A. A. Tseytlin, and M. Wolf, Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability , 0807.3228

View on Pith Pith review arXiv

[7] [6]

I. Bena, J. Polchinski, and R. Roiban, Hidden symmetries of the AdS(5) x S**5 superstring, Phys. Rev. D69 (2004) 046002, [ hep-th/0305116]

View on Pith Pith review arXiv 2004

[8] [7]

I. Adam, A. Dekel, L. Mazzucato, and Y. Oz, Integrability of type II superstrings on Ramond-Ramond backgrounds in various dimensions , JHEP 06 (2007) 085, [hep-th/0702083]

View on Pith Pith review arXiv 2007

[9] [8]

J.-G. Zhou, Super 0-brane and GS superstring actions on AdS(2) x S(2) , Nucl. Phys. B559 (1999) 92–102, [ hep-th/9906013]

View on Pith Pith review arXiv 1999

[10] [9]

J. Park and S.-J. Rey, Green-Schwarz superstring on AdS(3) x S(3) , JHEP 01 (1999) 001, [ hep-th/9812062]

View on Pith Pith review arXiv 1999

[11] [10]

J. Rahmfeld and A. Rajaraman, The GS string action on AdS(3) x S(3) with Ramond-Ramond charge, Phys. Rev. D60 (1999) 064014, [ hep-th/9809164]. – 25 –

View on Pith Pith review arXiv 1999

[12] [11]

G. Arutyunov and S. Frolov, Superstrings on AdS4xCP 3 as a Coset Sigma-model , JHEP 09 (2008) 129, [ 0806.4940]

View on Pith Pith review arXiv 2008

[13] [12]

j. Stefanski, B., Green-Schwarz action for Type IIA strings on AdS4 × CP 3, Nucl. Phys. B808 (2009) 80–87, [ 0806.4948]

View on Pith Pith review arXiv 2009

[14] [13]

P. Fre and P. A. Grassi, Pure Spinor Formalism for Osp(N—4) backgrounds , 0807.0044

View on Pith Pith review arXiv

[15] [14]

G. Bonelli, P. A. Grassi, and H. Safaai, Exploring Pure Spinor String Theory on AdS4 × CP3, JHEP 10 (2008) 085, [ 0808.1051]

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